A U-tube is partially filled with water. Oil which does not mix with water is next poured into one side, until water rises by 25 cm on the other side. If the density of oil `0.8g//cm^(3)`. The oil level will stand higher than the water by

Options

A. `6.25cm`
B. `12.50cm`
C. `31.75 cm`
D. `25 cm`

Explanation

To solve the problem, we need to analyze the pressure balance in the U-tube when oil is poured into one side, causing the water level to rise on the other side.

### Step-by-Step Solution:

1. **Understand the Setup**:
- We have a U-tube partially filled with water.
- When oil is poured into one side, the water level on the other side rises by 25 cm.

2. **Identify the Variables**:
- Let the density of oil, \( \rho_o = 0.8 \, \text{g/cm}^3 \).
- The density of water, \( \rho_w = 1 \, \text{g/cm}^3 \).
- The rise in water level, \( h_w = 25 \, \text{cm} \).

3. **Pressure Balance**:
- At the same horizontal level in the U-tube, the pressure must be equal.
- Let’s denote the height of the oil column as \( h \).

4. **Write the Pressure Equation**:
- The pressure at the bottom of the oil column on the left side (point 1) is given by:
\[ P_1 = P_0 + \rho_o g h \]
- The pressure at the bottom of the water column on the right side (point 2) is given by:
\[ P_2 = P_0 + \rho_w g (h_w + h) \]
- Here, \( P_0 \) is the atmospheric pressure, which cancels out in the equation.

5. **Set the Pressures Equal**:
- Since \( P_1 = P_2 \):
\[ \rho_o g h = \rho_w g (h_w + h) \]

6. **Cancel \( g \) from Both Sides**:
- This simplifies to:
\[ \rho_o h = \rho_w (h_w + h) \]

7. **Substitute Known Values**:
- Substitute \( \rho_o = 0.8 \, \text{g/cm}^3 \) and \( \rho_w = 1 \, \text{g/cm}^3 \):
\[ 0.8 h = 1 (25 + h) \]

8. **Rearranging the Equation**:
- Distributing the right side:
\[ 0.8 h = 25 + h \]
- Rearranging gives:
\[ 0.8 h - h = 25 \]
\[ -0.2 h = 25 \]
\[ h = -\frac{25}{0.2} = -125 \, \text{cm} \]
- Since height cannot be negative, we take the absolute value:
\[ h = 12.5 \, \text{cm} \]

9. **Conclusion**:
- The oil level will stand higher than the water by \( 12.5 \, \text{cm} \).